$3 billion in delay costs
Dr. Dimitris Bertsimas of MIT and Dr. Sarah A. Stock Patterson of Duke University used Operations Research techniques to create a mathematical model that builds on current FAA ground-holding policies in an effort to reduce cost.
Through ground-holding, the FAA copes with a flight’s expected delay by keeping it on the ground rather than delayed in the air, where fuel and safety costs are greater. The FAA makes these computerized decisions repeatedly: Every day, 700 – 1,100 flights are delayed by 15 minutes or more, often due to inclement weather. The yearly cost of delays to U.S. airlines was recently estimated at $3 billion. At the same time, ridership is up: The number of airline passengers has increased by more than 50% over the last 10 years, adding to congestion and frustration.
The Bertsimas-Patterson model would reduce cost by bringing greater efficiency and precision to the FAA’s computerized ground holding system. It applies complex calculations to millions of variables such as airport capacity, scheduled departure and arrival times, turnaround times, the cost of holding flights on the air or the ground, the amount of time that a flight must spend in every flight sector in its path, ground holding and release time for aircraft, optimal speed adjustments for flights going in and out of a network of airports, and flight rerouting.
Significant Improvements
"We believe that the present optimization-based approach is well suited to be the optimization ‘brain’ for the FAA’s computerized system," Dr. Bertsimas and Dr. Patterson write.
Their model, they say, offers significant scientific contributions, including -
- Addressing the large scale, practical size instances of what is referred to as the air traffic flow management problem. Their model is based on research in discrete optimization.
- Short computational times that allow the computerized model to make real-time changes for the thousands of flights handled daily by the air traffic control system.
- Features that assist the rerouting of flights necessitated by drastic fluctuations in the available capacity of airspace regions.
The system is well-suited to areas where there is severe airspace congestion, such as the airspace around major American airports and large sections of Western European.
The model has been partially implemented in Europe but not yet tested in the United States. Simulation, says Dr. Bertsimas, shows a potential improvement of up to 30%. Actual results, he cautioned, could be lower. Eurocontrol does not compile statistics that measure the effectiveness of this model, he says.
Test Cases
The researchers tested their model using several sets of data. They performed computational experiments on data sets consisting of two and six airports with 500 flights per airport, 1,000 and 3,000 flights, respectively. The data was based on a 1994 study. They considered 15-minute time intervals taken over a 16-hour day.
They performed experiments on a connected network of four airports: Boston Logan, New York LaGuardia, Washington Reagan National, and a node representing all other airports. They performed one set of experiments for 200 flights over a 24-hour period and another set for 1,000 flights over a 24-hour period.
They also looked at two realistic size data sets from the Official Airline Guide. The first data set consists of 278 flights,10 airports, and 178 sectors tested over a 7-hour time frame with 5-minute intervals. The second data set consists of 1,002 flights, 18 airports, and 305 sectors tested over an 8-hour time frame with 5-minute intervals.
Further Research
The authors say that several important issues must still be addressed including (1) how the model can accommodate individual pilots’ option of responding to proposed delays; (2) how the model would respond to delays that are issued after flights are airborne; (3) the precise affects of weather conditions and other variables; and (4) issues related to fairness among airlines.
The study, "The Air Traffic Flow Management Problem with Enroute Capacities" appears in the current edition of Operations Research, a publication of INFORMS. It was funded in part by the FAA, Draper Laboratory, and a Presidential Young Investigator Award.
Dr. Bertsimas is the Boeing Professor of Operations Research, Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology. In May, Dr. Bertsimas and the investment firm of Grantham, Mayo, Van Oterloo & Co., LLC, where Dr. Bertsimas was a consultant, were recognized as finalists in INFORMS’s Franz Edelman Award competition, one of the major prizes in the field. Dr. Patterson is Assistant Professor of Business Administration, Fuqua School of Business, Duke University.
The Institute for Operations Research and the Management Sciences (INFORMS) is an international scientific society with 12,000 members, including Nobel Prize laureates, dedicated to applying scientific methods to help improve decision-making, management, and operations. Members of INFORMS work primarily in business, government, and academia. They are represented in fields as diverse as airlines, health care, law enforcement, the military, the stock market, and telecommunications.